Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied,$\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system.

Process	Condition
$(I)$ Adiabatic	$(A) \Delta W = 0$
$(II)$ Isothermal	$(B) \Delta Q = 0$
$(III)$ Isochoric	$(C) \Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$
$(IV)$ Isobaric	$(D) \Delta U = 0$

In the $p-V$ diagram below,the dashed curved line is an adiabat. For a process that is described by a straight line joining two points $X$ and $Y$ on the adiabat (solid line in the diagram),heat is (Hint: consider the variation in temperature from $X$ to $Y$ along the straight line)

$A$ cylinder made of perfectly non-conducting material,closed at both ends,is divided into two equal parts by a heat-proof piston. Both parts of the cylinder contain the same mass of a gas at a temperature $t_0 = 27^{\circ}C$ and pressure $P_0 = 1 \text{ atm}$. If the gas in one of the parts is slowly heated to $t = 57^{\circ}C$ while the temperature of the first part is maintained at $t_0$,the distance moved by the piston from the middle of the cylinder will be $x \text{ cm}$. Find $x$ (total length of the cylinder $= 84 \text{ cm}$).

Match the List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. Pressure varies inversely with volume of an ideal gas.	$I$. Adiabatic process
$B$. Heat absorbed goes partly to increase internal energy and partly to do work.	$II$. Isochoric process
$C$. Heat is neither absorbed nor released by a system.	$III$. Isothermal process
$D$. No work is done on or by a gas.	$IV$. Isobaric process

$A$ certain amount of gas is taken through a cyclic process $(A-B-C-D-A)$ that has two isobars, one isochore, and one isothermal process. The cycle can be represented on a $P-V$ indicator diagram as:

Two gases have the same initial pressure,volume,and temperature. They expand to the same final volume,one adiabatically and the other isothermally.